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arXiv · 1312.6803

Solvable Lie groups of negative Ricci curvature

Y. Nikolayevsky·Yu. G. Nikonorov
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Abstract

We consider the question of whether a given solvable Lie group admits a left-invariant metric of strictly negative Ricci curvature. We give necessary and sufficient conditions of the existence of such a metric for the Lie groups the nilradical of whose Lie algebra is either abelian or Heisenberg or standard filiform, and discuss some open questions.

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BibTeXRIS

Y. Nikolayevsky, Yu. G. Nikonorov. 2013-12-24. Solvable Lie groups of negative Ricci curvature. https://doi.org/10.1007/s00209-015-1410-2

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